visualizing state transition graphs hannes pretorius visualization group, tu/e 17 october 2007...
TRANSCRIPT
![Page 1: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/1.jpg)
Visualizing State Transition Graphs
Hannes PretoriusVisualization Group, TU/e
17 October [email protected]
www.win.tue.nl/~apretori/
![Page 2: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/2.jpg)
Introduction
![Page 3: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/3.jpg)
![Page 4: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/4.jpg)
![Page 5: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/5.jpg)
![Page 6: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/6.jpg)
![Page 7: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/7.jpg)
![Page 8: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/8.jpg)
![Page 9: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/9.jpg)
![Page 10: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/10.jpg)
![Page 11: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/11.jpg)
![Page 12: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/12.jpg)
![Page 13: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/13.jpg)
![Page 14: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/14.jpg)
![Page 15: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/15.jpg)
![Page 16: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/16.jpg)
![Page 17: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/17.jpg)
State transition graph
Graph G = (V, E) where:• Node s in V is a possible system state• Directed edge t = (s, s’) in E is a
transition from source state s to target state s’
![Page 18: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/18.jpg)
Research question
“How can visualization be used to gaininsight into state transition graphs?”
![Page 19: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/19.jpg)
Research question
“How can visualization be used to gaininsight into state transition graphs?”
• What is insight?– Symmetries, patterns…
• What about size?– System behavior is often complex
• Typical users?– Small number of expert users
![Page 20: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/20.jpg)
![Page 21: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/21.jpg)
Related work
Van Ham et al., TVCG, 2002.
![Page 22: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/22.jpg)
Van Ham et al., TVCG, 2002.
![Page 23: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/23.jpg)
Approach
![Page 24: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/24.jpg)
![Page 25: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/25.jpg)
![Page 26: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/26.jpg)
Handle_posFront_wheel_po
sBack_wheel_po
sSeat_pos
= up= out= in= down
![Page 27: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/27.jpg)
Handle_posFront_wheel_po
sBack_wheel_po
sSeat_pos
= down= in= out= up
![Page 28: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/28.jpg)
State transition graph
Graph G = (V, E) where:• Node s in V is a possible system state• Directed edge t = (s, s’) in E is a
transition from source state s to target state s’
![Page 29: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/29.jpg)
State transition graph
Graph G = (V, E) where:• Node s in V is a possible system state• Directed edge t = (s, s’) in E is a
transition from source state s to target state s’
Every node s in V has:
• n associated attributes ai
• ai has domain Ai = {ai,1, …, ai,ki}
![Page 30: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/30.jpg)
Projection
Pretorius and Van Wijk, IV, 2005.
![Page 31: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/31.jpg)
![Page 32: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/32.jpg)
![Page 33: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/33.jpg)
![Page 34: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/34.jpg)
![Page 35: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/35.jpg)
![Page 36: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/36.jpg)
Projection
• Multivariate data:– Select interesting subset– Show low-dimensional projection
Pretorius and Van Wijk, IV, 2005.
![Page 37: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/37.jpg)
Projection
• Multivariate data:– Select interesting subset– Show low-dimensional projection
• Suggestive behavioral patterns• Meaning of positions projected to not
clear• Select subset based on domain
knowledgePretorius and Van Wijk, IV, 2005.
![Page 38: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/38.jpg)
Clustering
Pretorius and Van Wijk, InfoVis, 2006.
![Page 39: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/39.jpg)
![Page 40: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/40.jpg)
![Page 41: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/41.jpg)
![Page 42: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/42.jpg)
All states
Handle_pos
Seat_pos
![Page 43: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/43.jpg)
![Page 44: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/44.jpg)
![Page 45: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/45.jpg)
![Page 46: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/46.jpg)
![Page 47: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/47.jpg)
![Page 48: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/48.jpg)
![Page 49: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/49.jpg)
![Page 50: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/50.jpg)
![Page 51: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/51.jpg)
![Page 52: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/52.jpg)
Clustering
• Choose subsets based on domain knowledge
• Position clusters linearly• Show additional information on top of
this:– Clustering hierarchy– Arcs representing transitions– Bar tree representing size of clusters
Pretorius and Van Wijk, InfoVis, 2006.
![Page 53: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/53.jpg)
Clustering
• Reduce complexity– Location has meaning
• Patterns:– Attribute values– Behavior– Cluster sizes
• Different types of analysis:– Explorative (e.g. different perspectives)– Specific (e.g. deadlock analysis)
Pretorius and Van Wijk, InfoVis, 2006.
![Page 54: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/54.jpg)
Custom diagrams
Pretorius and Van Wijk, CG&A, 2007.Mathijssen and Pretorius, LNCS, 2007.
![Page 55: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/55.jpg)
Pretorius and Van Wijk, CG&A, 2007.Mathijssen and Pretorius, LNCS, 2007.
![Page 56: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/56.jpg)
Pretorius and Van Wijk, CG&A, 2007.Mathijssen and Pretorius, LNCS, 2007.
![Page 57: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/57.jpg)
Custom diagrams
• Support diagramming in general way:– Edit diagrams– Link with attributes
• Capture conceptualization of problem
Pretorius and Van Wijk, CG&A, 2007.Mathijssen and Pretorius, LNCS, 2007.
![Page 58: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/58.jpg)
Custom diagrams
• Support diagramming in general way:– Edit diagrams– Link with attributes
• Capture conceptualization of problem• Semantics clear and intuitive• Analysis and communication• Flexible Pretorius and Van Wijk, CG&A, 2007.
Mathijssen and Pretorius, LNCS, 2007.
![Page 59: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/59.jpg)
Wafer stepper Paint factory Petri nets
![Page 60: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/60.jpg)
Trace visualization
Submitted, PacificVis, 2008.
![Page 61: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/61.jpg)
![Page 62: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/62.jpg)
![Page 63: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/63.jpg)
Time
Att
ribu
tes
1 k
1n
1
2
![Page 64: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/64.jpg)
Time
Att
ribu
tes
1 k
1n
![Page 65: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/65.jpg)
![Page 66: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/66.jpg)
3
![Page 67: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/67.jpg)
Submitted, PacificVis, 2008.
![Page 68: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/68.jpg)
Trace visualization
• Traces:– Curb size and complexity– Users intuitively relate to time
Submitted, PacificVis, 2008.
![Page 69: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/69.jpg)
Trace visualization
• Traces:– Curb size and complexity– Users intuitively relate to time
• Three views:1. Diagram: easier to interpret2. Time series: general trends3. Transition graph: generalized behavior
Submitted, PacificVis, 2008.
![Page 70: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/70.jpg)
Conclusion
• Visualization of state transition graphs• Prototyping• Focus on state attributes
– Clear semantics
• Explorative analysis: – E.g. different perspectives
• Focused analysis:– E.g. deadlock, steam flow
![Page 71: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/71.jpg)
Questions
www.win.tue.nl/~apretori/
![Page 72: Visualizing State Transition Graphs Hannes Pretorius Visualization Group, TU/e 17 October 2007 a.j.pretorius@tue.nl apretori](https://reader035.vdocuments.mx/reader035/viewer/2022062417/551a7153550346761a8b4967/html5/thumbnails/72.jpg)
Projection (cont.)